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December, 1980 Laplace's Method Revisited: Weak Convergence of Probability Measures
Chii-Ruey Hwang
Ann. Probab. 8(6): 1177-1182 (December, 1980). DOI: 10.1214/aop/1176994579


Let $Q$ be a fixed probability on the Borel $\sigma$-field in $R^n$ and $H$ be an energy function continuous in $R^n$. A set $N$ is related to $H$ by $N = \{x \mid\inf_yH(y) = H(x)\}$. Laplace's method, which is interpreted as weak convergence of probabilities, is used to introduce a probability $P$ on $N$. The general properties of $P$ are studied. When $N$ is a union of smooth compact manifolds and $H$ satisfies some smooth conditions, $P$ can be written in terms of the intrinsic measures on the highest dimensional mainfolds in $N$.


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Chii-Ruey Hwang. "Laplace's Method Revisited: Weak Convergence of Probability Measures." Ann. Probab. 8 (6) 1177 - 1182, December, 1980.


Published: December, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0452.60007
MathSciNet: MR602391
Digital Object Identifier: 10.1214/aop/1176994579

Primary: 60B10
Secondary: 58C99

Keywords: Laplace's method , smooth manifold , weak convergence

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 6 • December, 1980
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